Micromechanical models of helical superstructures in ligament and tendon fibers predict large Poisson's ratios |
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| Authors: | Shawn P Reese Steve A Maas Jeffrey A Weiss |
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| Institution: | 1. Department of Bioengineering, and Scientific Computing and Imaging Institute University of Utah, 72 Salt Lake City, UT, USA;2. Department of Orthopaedics, University of Utah, Salt Lake City, UT, USA;1. Institute of Mechanical, Process and Energy Engineering, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, UK;2. Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France;3. Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory of Mechanics of Materials and Nanostructures, Thun, Switzerland;4. European Synchrotron Radiation Facility (ESRF), F-38043 Grenoble Cedex, France;5. Institute of Photonics and Quantum Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, UK;6. Institute for Surgical Technology and Biomechanics, University of Bern, Switzerland;1. Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA, USA;2. McKay Orthopaedic Research Laboratory, University of Pennsylvania, Philadelphia, PA, USA;1. School of Allied Health, Faculty of Health Science, Curtin University, Perth, Western Australia, Australia;2. School of Science, Engineering and Technology, RMIT University Vietnam, Ho Chi Minh City, Vietnam;3. Research Office, Curtin University, Perth, Western Australia, Australia;1. Department of Orthopaedic Surgery, University of Pennsylvania, 110 Stemmler Hall, 36th Street & Hamilton Walk, Philadelphia, PA 19104, United States;2. Department of Biomedical Engineering, Department of Orthopaedics and Rehabilitation, Pennsylvania State University, 205 Hallowell Building, University Park, PA 16802, United States;3. Eidgenössische Technische Hochschule, Rämistrasse 101, 8092 Zürich, Switzerland;4. Department of Bioengineering, 240 Skirkanich Hall, 210 South 33rd Street, University of Pennsylvania, Philadelphia, PA 19104, United States;5. Translational Musculoskeletal Research Center, Corporal Michael J. Crescenz Veterans Affairs Medical Center, 3900 Woodland Avenue, Philadelphia, PA 19104, United States;1. School of Biomedical Engineering, Dalhousie University, Halifax, Nova Scotia, Canada;2. Division of Engineering, Saint Mary’s University, Halifax, Nova Scotia, Canada;1. Institute of Bioengineering, School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK;2. Department of Musculoskeletal Biology, Institute of Ageing and Chronic Disease, University of Liverpool, Leahurst Campus, Neston CH64 7TE, UK;3. School of Biological Sciences, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, UK;4. Institute of Orthopaedics and Musculoskeletal Science, University College London, Stanmore HA7 4LP, UK |
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| Abstract: | Experimental measurements of the Poisson's ratio in tendon and ligament tissue greatly exceed the isotropic limit of 0.5. This is indicative of volume loss during tensile loading. The microstructural origin of the large Poisson's ratios is unknown. It was hypothesized that a helical organization of fibrils within a fiber would result in a large Poisson's ratio in ligaments and tendons, and that this helical organization would be compatible with the crimped nature of these tissues, thus modeling their classic nonlinear stress–strain behavior. Micromechanical finite element models were constructed to represent crimped fibers with a super-helical organization, composed of fibrils embedded within a matrix material. A homogenization procedure was performed to determine both the effective Poisson's ratio and the Poisson function. The results showed that helical fibril organization within a crimped fiber was capable of simultaneously predicting large Poisson's ratios and the nonlinear stress–strain behavior seen experimentally. Parametric studies revealed that the predicted Poisson's ratio was strongly dependent on the helical pitch, crimp angle and the material coefficients. The results indicated that, for physiologically relevant parameters, the models were capable of predicting the large Poisson's ratios seen experimentally. It was concluded that helical organization within a crimped fiber can produce both the characteristic nonlinear stress–strain behavior and large Poisson's ratios, while fiber crimp alone could only account for the nonlinear stress–strain behavior. |
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